3x(4x+2)=130

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Solution for 3x(4x+2)=130 equation: 


Simplifying
3x(4x + 2) = 130

Reorder the terms:
3x(2 + 4x) = 130
(2 * 3x + 4x * 3x) = 130
(6x + 12x2) = 130

Solving
6x + 12x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 6x + 12x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 6x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + 3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-65 + 3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-65 + 3x + 6x2 = 0

Solving
-65 + 3x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-10.83333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '10.83333333' to each side of the equation.
-10.83333333 + 0.5x + 10.83333333 + x2 = 0 + 10.83333333

Reorder the terms:
-10.83333333 + 10.83333333 + 0.5x + x2 = 0 + 10.83333333

Combine like terms: -10.83333333 + 10.83333333 = 0.00000000
0.00000000 + 0.5x + x2 = 0 + 10.83333333
0.5x + x2 = 0 + 10.83333333

Combine like terms: 0 + 10.83333333 = 10.83333333
0.5x + x2 = 10.83333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 10.83333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 10.83333333 + 0.0625

Combine like terms: 10.83333333 + 0.0625 = 10.89583333
0.0625 + 0.5x + x2 = 10.89583333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 10.89583333

Calculate the square root of the right side: 3.30088372

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.30088372 and -3.30088372.


Subproblem 1
x + 0.25 = 3.30088372

Simplifying
x + 0.25 = 3.30088372

Reorder the terms:
0.25 + x = 3.30088372

Solving
0.25 + x = 3.30088372

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 3.30088372 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 3.30088372 + -0.25
x = 3.30088372 + -0.25

Combine like terms: 3.30088372 + -0.25 = 3.05088372
x = 3.05088372

Simplifying
x = 3.05088372


Subproblem 2
x + 0.25 = -3.30088372

Simplifying
x + 0.25 = -3.30088372

Reorder the terms:
0.25 + x = -3.30088372

Solving
0.25 + x = -3.30088372

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -3.30088372 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -3.30088372 + -0.25
x = -3.30088372 + -0.25

Combine like terms: -3.30088372 + -0.25 = -3.55088372
x = -3.55088372

Simplifying
x = -3.55088372


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.05088372, -3.55088372}
Solution
x = {3.05088372, -3.55088372}

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